Thursday, July 3, 2014

Risk versus Uncertainty in Frank Knight’s Thought

Runde (1998) examines Frank Knight’s ideas on risk versus uncertainty.

In essence, Knight drew two distinctions, as follows:
(1) Risk
Risk involves being able to assign objective numeric probabilities, whether under a priori or relative frequency (statistical frequency) theories of probability.

(2) Uncertainty
Uncertainty is faced in situations where a person cannot assign objective numeric probabilities, because one cannot calculate such probabilities. (Runde 1998: 540).
Runde (1998) points to a subtle part of Knight’s thought on probability: Knight considered statistical probability (as obtained by relative frequencies) to be an intermediate type of probability between a priori probability and uncertainty (Runde 1998: 541). That is, according to Knight, there was a continuum of probability situations in Knight’s way of thinking (Runde 1998: 541).

But in the calculation of statistical probabilities, often the individual events or things grouped into a given reference class of events are far less homogenous than, say, the throws of a fair game of dice (Runde 1998: 541).

The problem, as Runde sees it, is that elsewhere Knight acknowledges a fundamental epistemological distinction between (1) a priori and (2) statistical (or relative frequency) probability. The first is a priori, but the latter is a posteriori (Runde 1998: 542).

The crucial point, then, is that the probabilities obtained on the basis of statistical probability are in a different epistemological category from the certainty of a priori probability: the relative frequency probabilities are a posteriori and the certainty that is found in a priori probabilities, such as in abstract and fair dice throws or roulette games, is absent (Runde 1998: 541).

In view of this, according to Runde, Knight’s “continuum” view of probability situations is severely undermined and must be rejected (Runde 1998: 542, 544).

The precondition for the calculation of an a priori probability is that we have a finite, exhaustive and exclusive number of outcomes which are all equiprobable, but one cannot necessarily do this with statistical (or relative frequency) probabilities, which remain in a different epistemological category.